We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+3
838
1
avatar

sin^2 0+sin^2 1+sin^2 2....sin^2 90

 Apr 20, 2015

Best Answer 

 #1
avatar+101771 
+8

$$\\sin^2 0+sin^2 1+sin^2 2....sin^2 90\\\\
=[sin^2 0+sin^2 1+...sin^244]\;\;\;+\;\;\;sin^245\;\;[+sin^246+....sin^2 90]\\\\
=(sin^2 0+sin^2 90)+....(sin^244+sin^246)+sin^245 \\\\
=(sin^2 0+cos^20)+....(sin^244+cos^244)\;\;+sin^245 \\\\
=(1)+....(1)\;\;+sin^245 \\\\
=45+sin^245\\\\
=45+(\frac{1}{\sqrt2})^2\\\\
=45\frac{1}{2}\\\\$$

.
 Apr 20, 2015
 #1
avatar+101771 
+8
Best Answer

$$\\sin^2 0+sin^2 1+sin^2 2....sin^2 90\\\\
=[sin^2 0+sin^2 1+...sin^244]\;\;\;+\;\;\;sin^245\;\;[+sin^246+....sin^2 90]\\\\
=(sin^2 0+sin^2 90)+....(sin^244+sin^246)+sin^245 \\\\
=(sin^2 0+cos^20)+....(sin^244+cos^244)\;\;+sin^245 \\\\
=(1)+....(1)\;\;+sin^245 \\\\
=45+sin^245\\\\
=45+(\frac{1}{\sqrt2})^2\\\\
=45\frac{1}{2}\\\\$$

Melody Apr 20, 2015

9 Online Users